Other European countries have drawn up bans on the burka and the niqab, but France is the first to put it into practice.
The law comes into effect at an already fraught moment in relations between the state and France’s Muslim minority, with president Nicolas Sarkozy accused of stigmatising Islam to win back votes from a resurgent far right.
Police said they arrested 59 people on Saturday, including 19 veiled women, who turned up for a banned protest in Paris over the law, while two more were detained as they attempted to travel to the rally from Britain and Belgium.
The new law says anyone refusing to lift his or her veil to submit to an identity check can be taken to a police station. There, officers must try to persuade them to remove the garment and can threaten fines.
A woman who repeatedly insists on appearing veiled in public can be fined 150 euros ($205) and ordered to attend re-education classes.
There are much more severe penalties for anyone found guilty of forcing someone else to hide his or her face “through threats, violence, constraint, abuse of authority or power for reason of their gender”.
Clearly aimed at fathers, husbands or religious leaders who force women to wear face veils, and applicable to offences committed in public or in private, the law imposes a fine of 30,000 euros and a year in jail.
Foreign extremists, including fugitive Al Qaeda leader Osama Bin Laden, have used the ban to argue France is at war with Islam and have called for attacks.